Measuring angles in triangles worksheet with eight problems requiring students to find the missing angle 'a°' using the triangle angle sum property.

I'll solve this worksheet by finding the missing angles in each of the 8 triangles. The key principle I'll use is that the sum of all interior angles in any triangle is always 180°.

Let me go through each problem one by one:

Problem 1:
- Given angles: 70° and 35°
- Missing angle 'a': 180° - 70° - 35° = 75°

Problem 2:
- Given angles: 82° and 44°
- Missing angle 'a': 180° - 82° - 44° = 54°

Problem 3:
- Given angles: 117° and 17°
- Missing angle 'a': 180° - 117° - 17° = 46°

Problem 4:
- This is an isosceles triangle (two sides marked equal)
- One base angle is 68°, so the other base angle is also 68°
- Missing angle 'a' (vertex angle): 180° - 68° - 68° = 44°

Problem 5:
- This is an isosceles triangle (two sides marked equal)
- One base angle is 42°, so the other base angle is also 42°
- Missing angle 'a' (vertex angle): 180° - 42° - 42° = 96°

Problem 6:
- This is an equilateral triangle (all three sides marked equal)
- All angles in an equilateral triangle are equal: 180° ÷ 3 = 60°
- Missing angle 'a': 60°

Problem 7:
- This shows an exterior angle 'a' adjacent to the triangle
- The two non-adjacent interior angles are 40° and 17°
- The exterior angle equals the sum of the two opposite interior angles: a = 40° + 17° = 57°
- Note: The interior angle at that vertex would be 180° - 57° = 123°, but since 'a' is labeled on the exterior, we want the exterior angle.

Problem 8:
- This shows an exterior angle 'a' adjacent to the triangle
- The two non-adjacent interior angles are 88° and 39°
- The exterior angle equals the sum of the two opposite interior angles: a = 88° + 39° = 127°

The solutions are:
1. 75°
2. 54°
3. 46°
4. 44°
5. 96°
6. 60°
7. 57°
8. 127°